Solve x2 + 8x -12 = 0 by completing the square
x2 + 8x =12 x2 + 8x + 16 =12 + 16
(x + 4)2 =28 x + 4 = + 28
{ -4 +2 x=-4 +2
6.3: Relationship of Roots,
Factoring, Graphing &
Solving Equations
If A*B = 0 thenA= 0 or B = 0
(x+2) (x-3) = 0(x+2)=0 or (x-3) = 0 x= -2 or x=3
Solve by factoring:
x2 – x - 6= 0
{-2, 3}
x2 – x - 6= 0
Factors: Solutions:Roots:Graph:
(x+2) (x-3){ -2,3}-2 and 3
x-int at -2 and 3
Equation:
Factors: Solutions:Roots:Graph:
p and q {p, q} (x-p)(x-q)
x-int at p and q
Equation:MULT. and make it = 0
Solve by
Factoring: 2x2 +7x = 152x2 +7x – 15 = 0
(2x-3) (x+5) = 0(2x-3)=0 or (x+5)= 02x=3 or x=-5 x=3/2 or x=-5
Solve by
Factoring: 5x2 – 60=5x5x2 - 5x – 60 = 05(x2 - x – 12) = 0
5(x-4) (x+3)= 0
5=0 x-4=0 or x+3= 0 x=4 or x=-3
Factors: Solutions:Roots:Graph:
{0, –5 }
Equation:
0 and -5
x(x+5)x2 + 5x = 0
x-int at 0 and -5
Write two equations that has roots of ½ and –3/4(x – ½) (x + 3/4 ) =0
x2 + 3x/4 – x/2 – 3/8 = 0
8x2 + 2x – 3 = 0
x2 + 1x/4 – 3/8 = 0
8 8 8
Find two consecutive odd integers whose product is 195x (x+2) = 195x2 + 2x = 195x2 + 2x – 195 = 0(x-13)(x+15) =0x-13 = 0 or x+15 =0x=13 x=-15
13 & 15 or -15 &-13
Factor by
graphing: 2x2 +7x - 15
2x2 +7x – 15 =yRoots: 3/2 and -5
Factors: (x – 3/2) (x+5)(2x – 3) (x + 5)
Check: 2x2 +7x - 15
Factor by
graphing: 4x2 - 100
4x2 - 100 =yRoots: 5 and -5
Factors: (x – 5) (x+5)
4(x – 5) (x + 5)
Check: x2 – 25 NO!